Wave Functions and Yukawa Couplings in Local String Compactifications

TL;DR

The work develops a local string-compactification framework for magnetised D7-branes in type IIB theory, exploiting explicit local metrics on 4-cycles to obtain analytic chiral wavefunctions by solving the Dirac and Laplace equations. Yukawa couplings are computed as triple overlaps of normalised wavefunctions, enabling direct evaluation of holomorphic and non-holomorphic contributions to the couplings. The authors study three local geometries, ${\mathbb P}^1\times{\mathbb P}^1$, ${\mathbb P}^2$, and the associated local Calabi–Yau spaces, for both supersymmetric and non-supersymmetric flux backgrounds with Abelian and non-Abelian bundles, detailing zero-mode counting, normalisation, and overlap integrals. The results illustrate how fluxes and geometry control the chiral spectrum and the structure of Yukawa matrices, with implications for phenomenology and neutrino physics through KK-mode effects and local flavour symmetries.

Abstract

We consider local models of magnetised D7 branes in IIB string compactifications, focussing on cases where an explicit metric can be written for the local 4-cycle. The presence of an explicit metric allows analytic expressions for the gauge bundle and for the chiral matter wavefunctions through solving the Dirac and Laplace equations. The triple overlap of the normalised matter wavefunctions generates the physical Yukawa couplings. Our main examples are the cases of D7 branes on P1xP1 and P2. We consider both supersymmetric and non-supersymmetric gauge backgrounds and both Abelian and non-Abelian gauge bundles. We briefly outline potential phenomenological applications of our results.